Two- and three-nucleon contact interactions and ground-state energies of light- and medium-mass nuclei

Classes of two-nucleon (2N) contact interactions are developed in configuration space at leading order (LO), next-to-leading order (NLO), and next-to-next-to-next-to-leading order (N3LO) by fitting the experimental singlet np scattering length and deuteron binding energy at LO, and np and pp scattering data in the laboratory-energy ranges 0–15 MeV at NLO and 0–25 MeV at N3LO. These interactions are regularized by including two Gaussian cutoffs, one for T=0 and the other for T=1 channels. The cutoffs are taken to vary in the ranges R0=(1.5–2.3) fm and R1=(1.5–3.0) fm. The 780 (1100) data points up to 15 (25) MeV energy, primarily differential cross sections, are fitted by the NLO (N3LO) models with a χ2/datum about 1.7 or less (well below 1.5), when harder cutoff values are adopted. As a first application, we report results for the binding energies of nuclei with mass numbers A=3–6 and 16 obtained with selected LO and NLO 2N models both by themselves as well as in combination with a LO three-nucleon (3N) contact interaction. The latter is characterized by a single low-energy constant that is fixed to reproduce the experimental 3H binding energy. The inclusion of the 3N interaction largely removes the sensitivity to cutoff variations in the few-nucleon systems and leads to predictions for the 3He and 4He binding energies that cluster around 7.8 and 30 MeV, respectively. However, in 16O this cutoff sensitivity remains rather strong. Finally, predictions at LO only are also reported for medium-mass nuclei with A=40, 48, and 90.